How to smooth out the slope between two fragments?
With your mesh selected go in to sculpt mode.

Choose the Smooth brush by pressing S, then LMB  and drag over the places you want smoothed.



If you do not want to use sculpt mode.

In edit mode, select all of the vertices, by pressing A A. Then click on the button on the tool shelf, on the Tools tab under Deform: called Smooth Vertex. You can adjust the number of iterations the smoothing runs in the bottom of the tool shelf, or by pressing F6.